Classification And Properties of Dual Conical Congruences
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To quickly assess the difficulty of the text, read a short excerpt:
Making use of the symbols defined by 2), 3), 4), § 3, we have immediately 4) S = 0.
Multiply •/2^=Oby3£at, subtract S.-^ (So 1 5i + $02^2 +$0353) = and then substitute in terms of the new coordinates. Making i successively equal l, 2, 3, we obtain the following equations: O3 3t22 ~f~ ^2 3t33 + Xi Q = , 5) Ss Xii — Si 3E33 + 3t2 ^ == , -52X11 + 51X22 +$3^ = 0.
By further examination of this system of equations 2), 4), 5), we find that, considering the system made up of 2) and 5), — 21 — the dete...rminants of the third order of the matrix of their coefficients -s.
s.
Xi s.
-5, X.
-s.
St X, Xl 3E.
Xs are all congruent to zero (mod 5); and therefore for the rays which are to be considered, these determinants must all be zero on account of 4), and hence the equations 2), 5) are not independent for any rays of the configuration. The determi- nants of the second order all vanish only if Si = X2 = S3 = 0, and in this case the whole system 2), 4), 5) is satisfied.
Since the point-rays all satisfy the system of equations 2), 4), 5), it is unsatisfactory for the determination of a closed configuration.
What to read after Classification And Properties of Dual Conical Congruences?
You can find similar books in the "Read Also" column, or choose other free books by Archie Burton Pierce to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Making use of the symbols defined by 2), 3), 4), § 3, we have immediately 4) S = 0.
Multiply •/2^=Oby3£at, subtract S.-^ (So 1 5i + $02^2 +$0353) = and then substitute in terms of the new coordinates. Making i successively equal l, 2, 3, we obtain the following equations: O3 3t22 ~f~ ^2 3t33 + Xi Q = , 5) Ss Xii — Si 3E33 + 3t2 ^ == , -52X11 + 51X22 +$3^ = 0.
By further examination of this system of equations 2), 4), 5), we find that, considering the system made up of 2) and 5), — 21 — the dete...rminants of the third order of the matrix of their coefficients -s.
s.
Xi s.
-5, X.
-s.
St X, Xl 3E.
Xs are all congruent to zero (mod 5); and therefore for the rays which are to be considered, these determinants must all be zero on account of 4), and hence the equations 2), 5) are not independent for any rays of the configuration. The determi- nants of the second order all vanish only if Si = X2 = S3 = 0, and in this case the whole system 2), 4), 5) is satisfied.
Since the point-rays all satisfy the system of equations 2), 4), 5), it is unsatisfactory for the determination of a closed configuration.
What to read after Classification And Properties of Dual Conical Congruences?
You can find similar books in the "Read Also" column, or choose other free books by Archie Burton Pierce to read onlineMoreLess
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